{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d7cd1786-3bfc-4453-94e2-f3be3b2355ab",
   "metadata": {},
   "source": [
    "Chapter 08\n",
    "\n",
    "# 平面几何变换\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "86455193-3d75-4c6b-8a72-7cf30e680f7d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2677c0fd-a1e5-46f8-bb9c-6cca75329d63",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lighten_color(rgb, percentage):\n",
    "    \"\"\"\n",
    "    让给定的 RGB 颜色变浅指定百分比。\n",
    "    \n",
    "    参数：\n",
    "        rgb (tuple): 原始 RGB 颜色，每个值在 [0, 1] 之间。\n",
    "        percentage (float): 变浅的比例，取值在 [0, 1] 之间。\n",
    "        \n",
    "    返回：\n",
    "        tuple: 变浅后的 RGB 颜色。\n",
    "    \"\"\"\n",
    "    # 确保输入的 RGB 值和百分比在合法范围\n",
    "    if not all(0 <= c <= 1 for c in rgb):\n",
    "        raise ValueError(\"RGB 值必须在 (0, 1) 范围内。\")\n",
    "    if not (0 <= percentage <= 1):\n",
    "        raise ValueError(\"百分比必须在 [0, 1] 范围内。\")\n",
    "    \n",
    "    # 计算新的 RGB 值\n",
    "    return tuple(c + (1 - c) * percentage for c in rgb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ac46222e-1d6d-457e-b644-d2e88cb6dc72",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 定义可视化函数\n",
    "def visualize(X_square_original,\n",
    "              X_grid, X_shape, title_txt):\n",
    "    fig, ax = plt.subplots()  # 创建绘图窗口\n",
    "    \n",
    "    # 绘制变换后的网格\n",
    "    for i in range(X_grid.shape[0]):\n",
    "        plt.plot(X_grid[i, :, 0], X_grid[i, :, 1], 'k-', linewidth=0.5)  # 绘制网格行\n",
    "    for j in range(X_grid.shape[1]):\n",
    "        plt.plot(X_grid[:, j, 0], X_grid[:, j, 1], 'k-', linewidth=0.5)  # 绘制网格列\n",
    "    \n",
    "    # 绘制变换后的散点，并用HSV色彩渲染\n",
    "    colors = plt.cm.hsv(np.linspace(0, 1, X_shape.shape[0]))  # HSV 色彩映射\n",
    "    for i in range(X_shape.shape[0]):\n",
    "        plt.plot(X_shape[i, 0], X_shape[i, 1], 'o', color=colors[i], markersize=4, zorder=1000)  # 绘制散点\n",
    "        plt.plot(X_square_original[i, 0], X_square_original[i, 1], 'o', color=lighten_color(colors[i], 0.78), markersize=4)\n",
    "        plt.plot((X_shape[i, 0],X_square_original[i, 0]),\n",
    "                 (X_shape[i, 1],X_square_original[i, 1]), lw = 0.25, color = lighten_color(colors[i], 0.78), zorder=1)\n",
    "    \n",
    "    # 绘制变换后的坐标轴方向向量\n",
    "    # plt.quiver(0, 0, X_vec[0, 0], X_vec[1, 0], angles='xy', scale_units='xy', scale=1, color=[0, 0.4392, 0.7529])  # 绘制第一个向量\n",
    "    # plt.quiver(0, 0, X_vec[0, 1], X_vec[1, 1], angles='xy', scale_units='xy', scale=1, color=[1, 0, 0])  # 绘制第二个向量\n",
    "    \n",
    "    # 绘制 x 和 y 轴\n",
    "    plt.axvline(x=0, color='k', zorder=0)  # 绘制 x 轴\n",
    "    plt.axhline(y=0, color='k', zorder=0)  # 绘制 y 轴\n",
    "    \n",
    "    # 设置标签和网格\n",
    "    # plt.ylabel('$x_2$')  # y轴标签\n",
    "    # plt.xlabel('$x_1$')  # x轴标签\n",
    "    # 移除 x 和 y 轴的刻度\n",
    "    ax.tick_params(axis='both', which='both', length=0, labelbottom=False, labelleft=False)\n",
    "    \n",
    "    # 移除 x 和 y 轴标签\n",
    "    ax.set_xlabel(\"\")\n",
    "    ax.set_ylabel(\"\")\n",
    "    ax.set_aspect(1)  # 设置坐标轴比例\n",
    "    ax.set_xlim([-3, 3])  # x轴范围\n",
    "    ax.set_ylim([-3, 3])  # y轴范围\n",
    "    ax.grid(linestyle='--', linewidth=0.15, color=[0.8, 0.8, 0.8])  # 添加网格\n",
    "    plt.title(title_txt)  # 设置图标题\n",
    "    # plt.savefig(title_txt + '.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7d3b4625-97b8-4c08-afb8-52e7dd276592",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_square_border_scatter(n):\n",
    "    \"\"\"\n",
    "    生成平面上正方形边框均匀排布的散点坐标，按顺时针顺序排列。\n",
    "\n",
    "    参数：\n",
    "        n (int): 每条边上的散点数。\n",
    "\n",
    "    返回：\n",
    "        np.ndarray: 一个二维数组，每行代表一个点，\n",
    "                    第一列为 x1 坐标，第二列为 x2 坐标。\n",
    "    \"\"\"\n",
    "    # 创建边框上的散点坐标\n",
    "    x = np.linspace(-1, 1, n)  # 边框坐标范围\n",
    "\n",
    "    # 上边框的点（从左到右）\n",
    "    top = np.column_stack((x, np.full_like(x, 1)))\n",
    "    # 右边框的点（从上到下）\n",
    "    right = np.column_stack((np.full_like(x, 1), np.flip(x)))\n",
    "    # 下边框的点（从右到左）\n",
    "    bottom = np.column_stack((np.flip(x), np.full_like(x, -1)))\n",
    "    # 左边框的点（从下到上）\n",
    "    left = np.column_stack((np.full_like(x, -1), x))\n",
    "\n",
    "    # 按顺时针顺序合并所有边框点\n",
    "    points = np.vstack((top, right, bottom, left))\n",
    "\n",
    "    return points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07b85ccf-0b79-47e4-bf63-d8c483ae2bbf",
   "metadata": {},
   "source": [
    "## 准备数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "169be63b-b643-44b4-89ac-3246a234278a",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 创建一个包含足够大的1x1网格区域\n",
    "x_vals = np.arange(-10,10+1)  # x轴网格点\n",
    "y_vals = np.arange(-10,10+1)  # y轴网格点\n",
    "X1, X2 = np.meshgrid(x_vals, y_vals)  # 生成网格\n",
    "X_grid = np.stack([X1, X2], axis=2)  # 将网格堆叠为3维数组"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ad500d0a-9564-4216-9551-5ce14346c1e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_vec = np.array([[1, 0],\n",
    "                  [0, 1]])  # 初始坐标轴向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "07326b71-0007-4b2b-9e21-c823370db86d",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_square = generate_square_border_scatter(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6a177455-baea-4428-817d-2442d501848d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 绘制原始网格、散点和坐标轴向量\n",
    "visualize(X_square,\n",
    "          X_grid, \n",
    "          X_square, \n",
    "          'Original Grid and Points')  # 绘制原始图像"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06ea5549-88af-4511-9ee5-9d374f346dea",
   "metadata": {},
   "source": [
    "## 平移"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f7dd6e01-f084-4169-a98e-af8b14103b95",
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = np.array([[-1.5],\n",
    "               [1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4b9e92ca-27d4-467a-8382-6474396807c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 绘制原始网格、散点和坐标轴向量\n",
    "visualize(X_square,\n",
    "          X_grid + t1.T, \n",
    "          X_square + t1.T, \n",
    "          'translation,t1')  # 绘制原始图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d9fb9a16-bcbc-4e4a-aa8a-23e4f6728d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "t2 = -t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6c57d87b-2917-48fc-8d25-d681032020d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 绘制原始网格、散点和坐标轴向量\n",
    "visualize(X_square,\n",
    "          X_grid + t2.T, \n",
    "          X_square + t2.T, \n",
    "          'translation,t2')  # 绘制原始图像"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "049c2ff1-f74c-4776-b130-04bf6996c8bd",
   "metadata": {},
   "source": [
    "## 等比例缩放"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "af36d763-d169-4770-9698-896602d9905b",
   "metadata": {},
   "outputs": [],
   "source": [
    "S_up = np.array([[2,0],\n",
    "                 [0,2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "10f5229a-b93d-4d8d-a9e7-b40071e4383e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 绘制原始网格、散点和坐标轴向量\n",
    "visualize(X_square,\n",
    "          X_grid @ S_up.T, \n",
    "          X_square @ S_up.T, \n",
    "          'uniform scaling up')  # 绘制原始图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8bdb29fd-f15b-419b-9f24-9d98c21b3eed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5, 0. ],\n",
       "       [0. , 0.5]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S_down = np.linalg.inv(S_up)\n",
    "S_down"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1e0c5131-7d8f-46ce-ba43-d4711b6a4d60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 绘制原始网格、散点和坐标轴向量\n",
    "visualize(X_square,\n",
    "          X_grid @ S_down.T, \n",
    "          X_square @ S_down.T, \n",
    "          'uniform scaling down')  # 绘制原始图像"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bb14571-c12d-4b1b-a62e-f71deb04a5df",
   "metadata": {},
   "source": [
    "## 旋转"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b8317818-a923-4307-8c3a-e0215707ee9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义一个函数，用于生成二维平面的旋转矩阵\n",
    "def rotation_matrix(theta):\n",
    "    \"\"\"\n",
    "    生成二维旋转矩阵\n",
    "    :param theta: 旋转角度（单位：弧度）\n",
    "    :return: 2x2旋转矩阵\n",
    "    \"\"\"\n",
    "    return np.array([[np.cos(theta), -np.sin(theta)],  # 第一行：[cos(theta), -sin(theta)]\n",
    "                     [np.sin(theta),  np.cos(theta)]])  # 第二行：[sin(theta), cos(theta)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "be130c15-ebbb-4e04-ae8d-70c952a7261d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义要旋转的角度（以弧度为单位）\n",
    "angle = 2* np.pi / 3  # 45度对应的弧度值\n",
    "\n",
    "# 调用函数生成对应的旋转矩阵\n",
    "R = rotation_matrix(angle)  # 计算45度旋转矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "340fe432-d1bd-41e5-b4f1-21d1bb077382",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_1 = np.array([[1],\n",
    "               [1]])\n",
    "\n",
    "## 绘制原始网格、散点和坐标轴向量\n",
    "visualize(X_square + t_1.T,\n",
    "          (X_grid + t_1.T) @ R.T, \n",
    "          (X_square + t_1.T) @ R.T, \n",
    "          'first translate, then rotate 120 deg')  # 绘制原始图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9ac5cc49-9b6c-4cbd-b654-9362b45d5fae",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
